Downing Street was digging in its heels on Sunday night and resisting growing pressure for MPs to be stripped of their ability to police their own affairs in the wake of a near tenfold reduction in the amount of overclaimed expenses Maria Miller was ordered to repay.

As the Conservative Grassroots organisation joined the former party chairman Lord Tebbit in calling for Miller to resign, Labour said that it would reform the system used to regulate MPs' expenses.

Angela Eagle, the shadow leader of the Commons, joined the former Labour cabinet minister Peter Hain in calling for reform after the Commons standards committee dramatically reduced the amount of money the culture secretary should repay for overclaiming on interest payments for her "second" home in Wimbledon, south-west London.

David Cameron, who said on Friday that all sides should "leave it there" over the Miller affair, rejected any change but is left at odds with his voters.

A Mail on Sunday/Survation poll found that 82% of Tories believed Miller should lose her job. A senior Tory source said: "We support the current system as it is. We are happy with the current system."

The prime minister appeared to be at odds too with Iain Duncan Smith, who said he was open to a proposal by Sir Ian Kennedy, the chairman of the Independent Parliamentary Standards Authority (Ipsa), to end the right of MPs to sit in judgment on their peers.

The work and pensions secretary told The Andrew Marr Show on BBC1: "I am very happy for that to be debated. I am among a number of those who feel this goes on and on and on eating away at the credibility of parliament.

"Whatever it takes to restore that credibility – I am very open to independent people looking at this. Personally I think the sooner we can get rid of this nonsense the better."

The calls for change came after the Commons standards committee, which includes 10 MPs and three non-voting lay members, said that the culture secretary should repay £5,800 instead of the £45,000 recommended by the parliamentary standards commissioner, Kathryn Hudson.

Sir Kevin Barron, the Labour chairman of the committee, and Hudson issued a joint statement on Friday to say that the amount had been agreed after Miller provided further details about her mortgage to the committee.

But Tebbit said that Miller, who was forced by the standards committee to apologise to MPs for her treatment of Hudson after she accused the commissioner of seeking to act beyond the law, should resign.

The former Tory chairman wrote on his Daily Telegraph blog: "Most members of the Commons must have hoped that the scandals over fiddled expenses had at least calmed down, even if not gone away.

"Now Mrs Miller has not just reignited the flames but, by the arrogance of her response to the scandal, poured petrol on the fire … The best way out of this is for Mrs Miller to resign."

Tebbit was joined by Conservative Grassroots, whose director, Ben Harris-Quinney, said: "There is no doubt that Maria Miller should now resign or be fired, the grassroots of the Conservative Party are resolute in calling for her to go with immediate effect.

"When the story broke that Maria Miller had abused her expenses allowance, because it was a Labour Member of Parliament that raised the issue, the Labour party faced accusations from Miller's staff of playing politics with the story for electoral gain.

"The polling data and conversations with grassroots Conservatives reveal a different story, that it is actually Conservative members and voters who want to see her held to account, to a greater degree than Labour or any other voters.

"Maria Miller is a totemic example of the modern political class who hold no discernible character, talent or integrity – the grassroots of the Conservative party have no time for careerist politicians who not only do not support, but flagrantly oppose, Conservative values once they are comfortably settled in parliament and cabinet.

"Maria Miller has discovered that she has no base of support in the Conservative party, other than in Downing Street, and no base of support in the country at large.

"Ironically, the longer she remains in her position the greater the damage will be to the Conservative party who are in fact her biggest detractors.

"It is therefore incumbent upon the leadership of the Conservative party to carry out the clear wishes of its members and remove Maria Miller with immediate effect."

The Daily Telegraph maintained the pressure on Miller on Sunday night by claiming she "flipped" the Wimbledon home at the heart of the expenses row – redesignated it to avoid paying capital gains tax when she sold it.

Miller had listed the property as her second home, allowing her to claim expenses towards the cost of the mortgage. Under guidance in place before the expenses scandal in 2009, MPs could declare such a property as their main residence to the tax authorities to avoid paying CGT on a sale. But the process of flipping homes, exposed by the Daily Telegraph when it uncovered the expenses scandal in 2009, prompted the parliamentary authorities to ask MPs to give an undertaking that they would pay CGT on the profits from any property on which they claimed expenses.

The Telegraph reported that the authorities wrote to Miller on three occasions to ask her to confirm that she would pay tax when she sold it. She subsequently redesignated the property and sold it at a profit of more than £1m earlier this year.

Labour indicated that it would maintain the pressure when it called for reform of the way MPs police their own affairs. It also wrote to Sir Jeremy Heywood, the cabinet secretary, to investigate claims that Miller's special adviser, Jo Hindley, tried to discourage the Daily Telegraph from investigating her expenses in light of the culture secretary's role in introducing the Leveson press reforms.

Eagle said: "We need a system which commands public confidence, and what we have at the moment clearly doesn't do that. We need reform so that people have faith that MPs are properly held to account. David Cameron has failed to act but Labour won't let this failing system go unreformed."

Labour appeared to be inching towards the proposal by the IPSA chief Sir Ian Kennedy who told the Sunday Times: "We have made great progress in cleaning up the problems of the past.

"To avoid further damage to parliament in the future, it should have the confidence to give away powers in regulating itself and see that independent regulation is the best, most transparent way forward."

A Conservative member of the standards committee said it would be wrong to outsource the power to regulate MPs on the grounds that it would allow outsiders to decide the composition of the commons. Geoffrey Cox, who is also a barrister, told the Westminster Hour on BBC Radio 4: "I think the problem is a constitutional one. Anybody who has the power to expel a member of parliament from the House of Commons has an enormous power to alter governments, to change the shape of political history. I think what the critics of the current system have to answer is if external regulation is going to be introduced, who is to do it, and to whom is that person or regulator to be accountable?"

Cox denied that the committee had been overly lenient with Miller. He said: "The consequences of what we found must be for others, but what cannot be said is that the committee was in any way deliberately or insincerely seeking to rescue the member from the consequences of her actions. That is for others to judge."

Peter Hain, Labour's reforming leader of the hHouse of Commons between 2003 and 2005, endorsed Kennedy's call. Hain told the Guardian: "I was very conscious, when leader of the commons, of the fact that parliament is sovereign constitutionally and jealously guards its independence from governments and judicial interference, for example through parliament privilege when speaking in the house. That is a really important principle to defend.

"The Maria Miller fiasco has just reincarnated the whole expenses scandal and the public strongly feel – and I think they are right – that this particular episode illustrates one rule for MPs and one rule for the rest of the population. That can't be right, it is not defensible and it brings MPs into disrepute."

Duncan Smith, who worked closely with Miller in her previous ministerial post as minister for the disabled, offered strong personal support for the culture secretary and said she had been the victim of "media antipathy" because of her role in overseeing the Leveson press reforms.

He said: "I am enormously fond of her. She has done a very good job in a very difficult set of circumstances with the Leveson inquiry that has stirred up a lot of media antipathy to her.

"And also the gay marriage stuff – there are a lot of Conservatives out there who, perhaps, were not necessarily in support of it all and so feel rather bitter about that. I have known her to be a reasonable and honest person."